第2关：两点透视

一. 任务描述

1. 本关任务

(1) 理解透视投影变换的方法; (2) 将main函数中的空白部分补充完整。

2. 输入

(1) 代码将自动输入一个边长为1的obj正方体模型，具体模型如下图：

(2) 代码自动将模型投影到二维平面中心生成一个边长为1的绿色立方体；

(3) 改变模型位置，产生两点透视: 将绿色立方体顶点分别沿y轴逆时针旋转45度，向y轴正方向平移1.2个单位，绘制一个红色立方体。再将红色立方体顶点分别向x轴正，负两个方向平移1.2个单位，绘制两个红色立方体。最后对三个红立方体进行投影变换，变换矩阵Projection已给出；

(4) 改变视点与模型位置，产生两点透视(先模型变换再观察变换)： 首先将立绿色方体的顶点分别向x轴正，负两个方向平移1.2个单位，绘制两个绿色立方体。然后对三个绿色立方体分别进行观察变换，将参数eye沿y轴顺时针旋转45度作为相机坐标，中心点坐标为center，向上矢量为Vec3f(0, 1, 0)。最后对三个绿立方体进行投影变换，变换矩阵Projection已给出；

(5) 改变视点与模型位置，产生两点透视(先观察变换再模型变换)： 首先对绿色立方体分别进行观察变换，将参数eye沿y轴顺时针旋转45度作为相机坐标，中心点坐标为center，向上矢量为Vec3f(0, 1, 0)。将绿色立方体向y轴负方向平移1.2个单位，绘制一个黄色立方体。再将黄色立方体顶点分别向x轴正，负两个方向平移1.2个单位，绘制两个黄色立方体。最后对三个黄立方体进行投影变换，变换矩阵Projection已给出。

3. 输出

具体结果如下图所示：

二. 相关知识

1. 透视投影

透视投影相关知识点，请参考教材与课件或有关资料。

三. 操作说明

(1) 按要求补全代码； (2) 点击窗口右下角"测评"按钮，等待测评结果，如果通过后可进行下一关任务。

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开始你的任务吧，祝你成功！

四.实验代码

#include <vector>
#include <cmath>
#include <algorithm>
#include <iostream>
#include "model.h"
#include "geometry.h"
#include "pngimage.h"

using namespace std;
const double PI = acos(-1.0);

void line(Vec3i p0, Vec3i p1, PNGImage  &image, PNGColor color)
{
	bool steep = false;
	if (std::abs(p0.x - p1.x) < std::abs(p0.y - p1.y))
	{
		std::swap(p0.x, p0.y);
		std::swap(p1.x, p1.y);
		steep = true;
	}
	if (p0.x > p1.x)
	{
		std::swap(p0.x, p1.x);
		std::swap(p0.y, p1.y);
	}

	int dx = p1.x - p0.x;
	int dy = std::abs(p1.y - p0.y);

	int y = p0.y;
	int d = -dx;
	for (int x = p0.x; x <= p1.x; x++)
	{
		if (steep)
			image.set(y, x, color);
		else
			image.set(x, y, color);

		d = d + 2 * dy;
		if (d > 0)
		{
			y += (p1.y > p0.y ? 1 : -1);
			d = d - 2 * dx;
		}
	}
}

Matrix projection(Vec3f eye, Vec3f center)
{
	Matrix m = Matrix::identity(4);
	m[3][2] = -1.f / (eye - center).norm();
	return m;
}

Matrix viewport(int x, int y, int w, int h, int depth) {
	Matrix m = Matrix::identity(4);
	m[0][3] = x + w / 2.f;
	m[1][3] = y + h / 2.f;
	m[2][3] = depth / 2.f;

	m[0][0] = w / 2.f;
	m[1][1] = h / 2.f;
	m[2][2] = depth / 2.f;
	return m;
}

Matrix lookat(Vec3f eye, Vec3f center, Vec3f up) {
	Vec3f z = (eye - center).normalize();
	Vec3f x = (up^z).normalize();
	Vec3f y = (z^x).normalize();
	Matrix res = Matrix::identity(4);
	for (int i = 0; i < 3; i++) {
		res[0][i] = x[i];
		res[1][i] = y[i];
		res[2][i] = z[i];
		res[i][3] = -center[i];
	}
	return res;
}

Matrix translation(Vec3f v) {
	Matrix Tr = Matrix::identity(4);
	Tr[0][3] = v.x;
	Tr[1][3] = v.y;
	Tr[2][3] = v.z;
	return Tr;
}

Matrix scale(float factorX, float factorY, float factorZ)
{
	Matrix Z = Matrix::identity(4);
	Z[0][0] = factorX;
	Z[1][1] = factorY;
	Z[2][2] = factorZ;
	return Z;
}

Matrix rotation_x(float angle)
{
	angle = angle * PI / 180;
	float sinangle = sin(angle);
	float cosangle = cos(angle);

	Matrix R = Matrix::identity(4);
	R[1][1] = R[2][2] = cosangle;
	R[1][2] = -sinangle;
	R[2][1] = sinangle;
	return R;
}

Matrix rotation_y(float angle)
{
	angle = angle * PI / 180;
	float sinangle = sin(angle);
	float cosangle = cos(angle);

	Matrix R = Matrix::identity(4);
	R[0][0] = R[2][2] = cosangle;
	R[0][2] = sinangle;
	R[2][0] = -sinangle;
	return R;
}

Matrix rotation_z(float angle) {
	angle = angle * PI / 180;
	float sinangle = sin(angle);
	float cosangle = cos(angle);

	Matrix R = Matrix::identity(4);
	R[0][0] = R[1][1] = cosangle;
	R[0][1] = -sinangle;
	R[1][0] = sinangle;
	return R;
}

int main(int argc, char** argv)
{
	const PNGColor white = PNGColor(255, 255, 255, 255);
	const PNGColor black = PNGColor(0, 0, 0, 255);
	const PNGColor red = PNGColor(255, 0, 0, 255);
	const PNGColor green = PNGColor(0, 255, 0, 255);
	const PNGColor blue = PNGColor(0, 0, 255, 255);
	const PNGColor yellow = PNGColor(255, 255, 0, 255);

	Model *model = NULL;
	const int width = 800;
	const int height = 800;
	const int depth = 255;


	//generate some image
	PNGImage image(width, height, PNGImage::RGBA); //Error when RGB because lodepng_get_raw_size_lct(w, h, colortype, bitdepth) > in.size() in encode
	image.init(black);
	model = new Model("cube.obj");

	Vec3f eye(0, 0, 4);
	Vec3f center(0, 0, 0);
	Matrix ModelView = Matrix::identity(4);
	Matrix Projection = projection(eye, center);
	Matrix ViewPort = viewport(width / 4, width / 4, width / 2, height / 2, depth);

	for (int i = 0; i < model->nfaces(); i++)
	{
		std::vector<int> face = model->face(i);
		for (int j = 0; j < (int)face.size(); j++)
		{
			Vec3f wp0 = model->vert(face[j]);
			Vec3f wp1 = model->vert(face[(j + 1) % face.size()]);

			Matrix S0 = scale(0.4, 0.4, 0.4);
			Vec3f swp0 = S0 * wp0;
			Vec3f swp1 = S0 * wp1;
            float fx[3]={-1.2,0,1.2};
            // Please add the code here
            /********** Begin ********/
            


            //绿色
            Vec3f eye_xz= rotation_y(-45)*eye ;
            Matrix ModelView4 = lookat(eye_xz, center, Vec3f(0, 1, 0)); //视图变换矩阵
            Matrix Projection4 = projection(eye_xz, center);
            for(int i=0;i<3;i++){
                Matrix T4 = translation(Vec3f( fx[i],0, 0));
                Vec3f tr40 = ViewPort * Projection4 * ModelView4 * T4 *swp0;
                Vec3f tr41 = ViewPort * Projection4 * ModelView4 * T4 *swp1;
                line(tr40,tr41, image, green);//绿色

                Matrix R3 =rotation_y(45);//沿y轴逆时针旋转45度
                Matrix T3y =translation(Vec3f (fx[i],1.2,0));//向y轴正方向平移1.2个单位
                Vec3f tr30= ViewPort * Projection * T3y * R3 * swp0;
                Vec3f tr31= ViewPort * Projection * T3y * R3 * swp1;
                line(tr30,tr31, image, red);//红色

                Matrix T5y =translation(Vec3f (fx[i],-1.2,0));//向y轴负方向平移1.2个单位
                Vec3f tr50 = ViewPort * Projection4 * T5y *ModelView4 *swp0;
                Vec3f tr51 = ViewPort * Projection4 * T5y* ModelView4 *swp1;
                line(tr50,tr51, image, yellow);//黄色

            }

            
            



			
            /********** End ********/
		}
	}

	image.flip_vertically(); // i want to have the origin at the left bottom corner of the image
	image.write_png_file("../img_step2/test.png");
	delete model;
	return 0;
}